A nickel -titanium alloy is made to be wholly or substantially free of titanium-rich oxide inclusions by including yttrium in an amount up to 0.15 wt. %, with the balance of the alloy being nickel and titanium in approximately equal proportion. For example, a NiTiY alloy may have a composition including, in weight percent based on total alloy weight: between 50 and 60 wt. % nickel; between 40 and 50 wt. % titanium; and between 0.01 and 0.15 wt. % yttrium. The resulting alloy is capable of being drawn into various forms, e.g., fine medical-grade wire, without exhibiting an unacceptable tendency to develop surface defects or to fracture or crack during cold drawing or forging. The resulting final forms exhibit favorable fatigue strength and fatigue-resistant characteristics.